Surface relaxation in ferroelectric perovskites

Lattice relaxation on the surface of PbTiO₃ and BaTiO₃ is investigated under the assumption that the spurious lattice expansion in perovskite nanocrystals is caused by the surface relaxation. By comparing the observed peak position and full width at half maximum with those of the calculated x-ray diffraction patterns from a cubic lattice containing surface relaxation, the maximum relaxation on the surface of PbTiO₃ is found to be 0.035 nm, and 0.015 nm for BaTiO₃. The relaxation is decreased to $1/e$ at 1.5 layers in PbTiO₃ and 8 layers in BaTiO₃. These values are consistent with the extrapolation lengths predicted by a modified Landau theory explaining the size effect on the phase transition temperature.